Line a baking sheet with parchment paper. In a large saucepan, combine the milk, butter, salt, and black pepper over medium-high heat. Bring to a boil, then remove from the heat, add the flour, and with a wooden spoon, stir briskly for about 1 minute to incorporate. Return to the heat and continue stirring for 1 minute, over medium-high heat. Remove from the heat and add the eggs one at a time, beating after each addition. Add the cheese and ham and beat until it is incorporated and a slightly soft dough forms. Drop the dough by the spoonful onto the prepared baking sheet to form a ring (about 12 to 14 spoonfuls. Bake for 10 minutes, then reduce the oven temperature to 350 degrees F. and bake until golden brown, about 25 minutes.